GOOSE CREEK, South Carolina (CNN) -- Two men faced state explosives charges Sunday after police outside Charleston, South Carolina, found what a law enforcement source said was a bomb and bomb-making material in their car during a weekend traffic stop.

"They're going to be formally charged tomorrow with state charges by the Berkeley County Sheriff's Office, and those charges will involve explosives," Berkeley County Chief Deputy Butch Henerey told CNN.

But federal officials disputed that account, telling CNN that there was no bomb.

And FBI spokesman Richard Kolko told CNN, "We have not found a clear link to terrorism."

The incident began about 5:30 p.m. Saturday, when the men's vehicle was pulled over along U.S. Highway 176 in Goose Creek, about 20 miles north of Charleston, for speeding, police said.

The law enforcement source, who insisted on anonymity, said the materials included at least one bomb and a number of bomb-making elements, including chemicals capable of being used in the production of bombs, fuses and igniters -- small gunpowder charges used to ignite some explosives.

The Charleston County bomb squad responded, and traffic was halted along the road for 10 hours until the materials were detonated, reporter Venton Blandin of CNN affiliate WCIV said. He described the sound of the detonation as "fairly small."

Police identified the men as Yousef Megahed, 21, and Ahmed Mohamed, 24, neither of whom is a U.S. citizen. They were being held at the Berkeley County Detention Center in Moncks Corner, South Carolina.

But federal officials cast doubt on the South Carolina authorities' account Sunday night.

Federal law enforcement sources familiar with the case said no bomb was found -- but the men arrested did not have ready explanations for materials found in the vehicle. That raised questions, which prompted local officials to contact the FBI and Joint Terrorism Task Force, the sources said.